How far a line of sight reaches

Adapted from IOAA 2015 (Magelang), theory problem 14. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.

Suppose we lived in a static, infinitely large universe in which the average number of stars is $n={10}^9$ per cubic megaparsec and every star has the radius of the Sun, $6.957\times {10}^8$ m. Assume that ordinary Euclidean geometry holds. How far, on average, could we see in any direction before the line of sight met a star? Give the answer in Mpc.

AnswerThe average line of sight would reach $6.26\times {10}^{17}$ Mpc before meeting a star. Light takes about $2.04\times {10}^{24}$ years to cross that distance, far longer than the age of the Universe, so in our Universe most lines of sight reach no star, which is why the night sky is dark.